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© Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1: Ethylene Refrigeration and Compression in an Olefin Plant: A Gross.

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Presentation on theme: "© Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1: Ethylene Refrigeration and Compression in an Olefin Plant: A Gross."— Presentation transcript:

1 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1: Ethylene Refrigeration and Compression in an Olefin Plant: A Gross Error Detection Problem Using Observability and Redundancy Analysis *Flowsheet taken from Romagnoli & Sanchez “Data Processing and Reconciliation for Chemical Process Operations”, page 228.

2 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 1 5 2 3 4 6 F1 F2 F4 F3 F5F6 F12 F10 F13 F14 F7 F11 F15 F9 F8

3 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 F34 7 8 9 11 F21 F22 F63 F33 F32 F31F30 F29 F28 F19 F26 F15 F27 F35 F36 F16 F24 F23 F25 F18 F20 F17 15 14 12 13 10 F61 F37

4 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 F15 Case Study #1 312019 18 17 16 F39 F60F59F62 F58 F57F56 F54 F48 F55 F38 F61

5 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 F51 2524 2122 23 27 26 282930 F50 F53 F52 F49 F48 F47 F46 F63 F45 F44 F43 F42 F38 F41F40 F62F39

6 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 StreamVarianceMeasurementStreamVarianceMeasurement 110.8772.15210.00020.0278 20.2037.103220.0181.071 70.39712.92240.092.444 82.62435.98250.0142.621 95.7645.32260.361.711 120.92223.53270.5638.543 130.00060.0765280.0231.424 141.0518.92290.0081.101 151.4437.24301.10321.75 160.70620.88310.39712.58 170.0170.1643320.1524.999 180.138.420360.096.398 190.094.102450.134.250 200.0141.931521.23216.34 Table 1.1: Data for measured flows

7 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1

8 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Mass Balances: 1)y 1 – z 1 – z 2 = 0 2)z 1 – z 3 – z 4 = 0 3)y 2 + z 2 + z 3 + z 4 + y 3 – y 4 – y 5 = 0 4)y 4 + z 5 – z 6 – y 6 = 0 5)z 6 – y 3 – z 5 = 0 6)y 5 – y 7 – y 8 – y 9 = 0 7)y 9 – y 10 – z 9 = 0 8)z 9 – y 11 – z 10 = 0 9)z 10 – y 12 – y 14 – y 26 = 0 10)y 26 – z 7 – y 17 – y 18 = 0 11)y 17 – y 15 – y 16 – y 19 = 0 12)y 14 + y 16 + z 7 – y 13 = 0 13)y 10 + y 11 + y 12 + y 18 + y 19 – y 20 – y 21 – y 22 – y 23 = 0 14)y 23 – y 24 – y 25 – z 8 = 0 15)y 21 + y 22 + y 24 + y 25 + z 8 + z 35 – z 11 – z 33 = 0 16)z 12 + z 33 – z 27 = 0 17)z 26 + z 27 – z 21 = 0

9 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Mass Balances: 18)z 28 – z 26 – z 29 – z 30 = 0 19)z 32 – z 31 = 0 20)z 29 + z 31 + z 34 – z 28 = 0 21)z 21 – z 20 – z 22 = 0 22)z 20 – z 18 – y 27 = 0 23)z 22 + z 24 – z 23 = 0 24)z 23 – y 28 = 0 25)y 28 – z 24 – z 25 = 0 26)z 18 – z 16 – z 35 = 0 27)z 27 – z 17 – z 19 = 0 28)z 16 + z 17 – z 15 = 0 29)z 15 – z 12 – z 14 = 0 30)z 14 – z 13 – z 34 = 0 31)z 17 + z 30 –z 32 = 0

10 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

11 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

12 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

13 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

14 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

15 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

16 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

17 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

18 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

19 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 F 31, F 32, F 45, and F 52 are NONREDUNDANT

20 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 GROSS ERROR!

21 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Testing measurement F 1 for gross error using serial elimination:

22 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Testing all measurements for gross error using serial elimination results in: Gross error detected in F 9 !

23 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Calculating the bias in F 9 : Therefore, the adjusted value of F 9 is given as: After adjustment, NO MORE GROSS ERROR!!

24 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 StreamReconciled with Bias Reconciled Without bias StreamReconciled with Bias Reconciled Without Bias 170.887072.8169210.0276 27.07947.1155221.05141.0496 712.861912.8784242.54222.5512 836.364136.2551252.62662.6285 954.464256.5556261.46331.4740 1223.502223.3768278.23738.4258 130.07560.0765281.41151.4192 1417.375118.8556291.09671.0993 1537.013537.62353022.151122.5204 1620.335620.79563112.5800 170.15120.1623324.9990 188.31988.4045366.29236.3393 194.08944.1312454.2500 201.91461.92195216.3400 Table 1.2: Reconciled data with and without bias

25 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Rank(A z ) = 24

26 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004

27 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 The zero rows in R 1 -1 R 2 indicate that F23, F33, F34, F35, and F50 may be estimated independently of the indeterminable variables: F 23 = 1.1597 F 33 = 4.9414 F 34 = 16.8279 F 35 = 16.6657 F 50 = 16.34

28 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 MATLAB code used to solve Case Study #1: y=[72.15;7.103;12.92;35.98;45.32;23.53;0.0765;18.92;37.24;20.88;0.1643;8.420;4.102;1.931;0.0278;1.071;2.444;2.621;1.711;8.543;1.424;1.101;22.75;12.58;4.999;6.398;4.25;16.34]; *** To obtain new values for yhat, objective function, etc., add bias of 11.2356 to measurement y 5 *** V=[10.87 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0.203 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0.397 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 2.624 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 5.76 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0.922 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0.0006 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 1.05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 1.44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0.706 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0.017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0.13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0.09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0.014 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0002 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.018 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.09 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.014 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.36 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.563 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.023 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.008 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.103 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.397 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.152 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.09 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.13 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.232];

29 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Ay=[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 1 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 1 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 -1 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 -1 -1 -1 -1 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

30 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 Az=[-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1;0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 0 1 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 - 1 1 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0];

31 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 [Q,R,E]=qr(Az); for I=1:31, for J=1:24, Q1(I,J)=Q(I,J); end; for I=1:31, for J=25:31, Q2(I,J-24)=Q(I,J); end; for I=1:24, for J=1:24, R1(I,J)=R(I,J); end;

32 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 for I=1:24, for J=25:35, R2(I,J-24)=R(I,J); end; G=Q2'*Ay; yhat=y-V*G'*inv(G*V*G')*G*y; Vr=G*V*G'; r=G*y; tau=r'*inv(Vr)*r; Id=[1 0 0 0 0 0 0;0 1 0 0 0 0 0;0 0 1 0 0 0 0;0 0 0 1 0 0 0;0 0 0 0 1 0 0;0 0 0 0 0 1 0;0 0 0 0 0 0 1];

33 © Universidad de Guanajuato, Mexico© University of Ottawa, Canada, 2004 Case Study #1 for I=1:28, for J=1:7, Ac(J,1)=G(J,I); end; Vri=inv(Vr)*(Id-Ac*inv(Ac'*inv(Vr)*Ac)*Ac'*inv(Vr)); O(I)=r'*Vri*r; end; B=[0;0;0;0;1;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0]; P=G*B; m=inv(P'*inv(G*V*G')*P)*P'*inv(G*V*G')*G*y; zr=-inv(R1)*Q1'*Ay*yhat;

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